Can you rotate an object in a way that can't be undone with subsequent rotations...

can you rotate an object in a way that can't be undone with subsequent rotations? maybe rotating it through a higher dimension or something?

Other urls found in this thread:

en.wikipedia.org/wiki/Gimbal_lock
twitter.com/NSFWRedditImage

If you could rotate it in a higher dimension, and no one else could, that would meet your criteria.

But you can't, so no.

>But you can't
you don't know me, watch me try.

If you project it to a 2d plane, information is lost so out can't be undone

This, rotate a ball and take a photo of it

You're basically asking if rotation is not necessarily revirsable

well is it?

Rotations are always reversible.

but the question was what if they weren't

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That's like asking for a triangle with a number of sides not equal to three.

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Sure. Take a piece of paper, set it on fire and rotate it concurrently of its immolation. Once the paper is destroyed you can't rotate it any further. :^)

check mate, m8

>reversion
>inverse
>inverse is still one of the rotations in set

sure. If you get infinity involved. Rotate an object about an axis that is infinitely far away from the object. The object will just keep moving in a straight line and practically never return.

There is no "practically" in mathematics.

There is if I define it. :^)

bingo
don't think of it as an reversible just another possible rotation
/thread

>can't be undone
Can't be undone uniquely
Ftfy

yeah i could rotate ur neck lol

I think rotations all belong to the SO(n) group so they have to be invertible

>I think
go away descartes, come back when u have facts.

How about rotations of objects on fucked up manifolds?
Kerr-Metric comes to mind

You could probably come up with some generalisation of rotations that aren't invertible, but a proper rotation is invertible by definition.

Ive been looking for a pic like this for Literally years. thatnks man

are you literally retarded? lmao

People don't think rotations be like they is, but it do.

i have something for you to rotate

Gimbal lock is related to this

en.wikipedia.org/wiki/Gimbal_lock

A rotation is defined to be an automorphism in an appropriate category. They are a priori reversible. The best you can do is ask for an endomorphism which is irreversible, like folding your shape onto itself and gluing it. Any non-monomorphic epimorphism will do, actually, although some categories have epimorphisms which are also monic and not invertible (including the category of topological spaces).

>Rotate an object about an axis that is infinitely far away from the object.

This is just a translation, brainlet. Translations are reversible too.

Gimbal locking only occurs because you apply 3 rotations one after another. It doesn't have anything to do with them being irreversible.

it wouldn't be a rotation

>fucked up manifold
looks straightforward user. The cube has orientation and direction. The "legs" have 2 main points where the :[math]\nabla[/math]" will change for what the cubes position is. There's a period for the whole function for gods sake

>"∇"

Generalize "rotation" to "length preserving linear mapping" and "something that can't be undone" to "linear mappings with a non-zero kernel". Then you clearly can't have a transform T that is both. If v is non-zero and in the kernel then the length of v is not zero but the length of Tv is.

The picture I posted is a visualization of the dirac belt trick. It has nothing to do with the kerr-metric which is the space-time metric of a rotating black hole.

Sorry for the misleading picture, had nothing else manifold-related to post.